Particle Filter for Plasma Insulin Estimation

2010 ◽  
Author(s):  
Kiriakos Kiriakidis
Keyword(s):  
Particle Filter ◽  
Posterior Probability ◽  
Compartmental Model ◽  
Bayesian Estimator ◽  
State Equations ◽  
Insulin In Plasma ◽  
Posterior Probability Density ◽  
Non Gaussian ◽  
Nonlinear State ◽  
Physiologic System

Bergman’s Minimal Model (MM) captures simply but accurately the homeostasis of glucose and insulin in plasma. The MM has been proposed as an estimator of insulin for Diabetes Mellitus. Along this line of research, the present work takes into account the error between Bergman’s simple compartmental model and the complex physiologic system it depicts. The author employs a Particle Filter (PF) in order to construct the posterior probability density of insulin from data. As a sequential Bayesian estimator, the PF can handle nonlinear state equations, such as the MM, as well as non-Gaussian modeling error. These advantages of the PF over the Kalman Filter warrant further consideration for insulin estimation and, in turn, avoidance of hyperinsulinemia.

An Improved Approach of Terrain-Aided Navigation Based on RBPF

2013 ◽  
Vol 336-338 ◽  
pp. 336-342
Author(s):  
Yi Gui ◽  
Nong Cheng
Keyword(s):  
Particle Filter ◽  
Posterior Probability ◽  
Transition Process ◽  
Shuttle Radar Topography Mission ◽  
Initial Position ◽  
Accurate Estimation ◽  
Extreme Conditions ◽  
Posterior Probability Density ◽  
Posterior Probability Density Function ◽  
Nonlinear State

Rao-Blackwellized Particle Filter (RBPF) is suitable for solving the linear/nonlinear mixed Terrain-Aided Navigation (TAN) problem. But the Particle Filter (PF) part of RBPF is Standard Particle Filter (SPF), causing particle diversity reduction and even filters divergence under extreme conditions. To get a better estimation of the errors of INS, this paper proposes an improved approach called Regularized Rao-Blackwellized Particle Filter (RRBPF). After updating the nonlinear state and corresponding importance weights, RRBPF resamples from the Epanechnikov kernel and then get the resampled particles through a linear transition process. Theoretically, the resampling part of RRBPF is equivalent to resampling from the approximated continuous posterior probability density function. Shuttle Radar Topography Mission (SRTM) terrain data is used in simulations to investigate the performance of RRBPF. Results show that RRBPF can provide more accurate estimation of TAN and bear larger initial position error than Sandia Inertial Terrain Aided Navigation (SITAN).

A New Adaptive UPF Algorithm through Improved Relative Entropy

2013 ◽  
Vol 658 ◽  
pp. 569-573
Author(s):  
Wen Tao Yu ◽  
Jun Peng ◽  
Xiao Yong Zhang
Keyword(s):  
Particle Filter ◽  
Relative Entropy ◽  
Particle Number ◽  
Time Step ◽  
Unscented Particle Filter ◽  
Posterior Probability Density ◽  
The Difference ◽  
Particle Filter Algorithm ◽  
Non Gaussian ◽  
Number Of Particles

Unscented particle filter (UPF) has high accuracy of state estimation for nonlinear system with non-Gaussian noise. While the computation of traditional unscented particle filter is huge and this depends on the particle number. In this paper we propose a new adaptive unscented particle filter algorithm AUPF through improved relative entropy which can adaptively adjust the particle number during filtering. Firstly the relative entropy is used to measure the distance between the posterior probability density and the importance proposal and the least number of particles for the next time step is decided according to the relative entropy. Then the least number is adjusted to offset the difference between the importance proposal and the true distribution. This algorithm can effectively reduce unnecessary particles meanwhile reduce the computation. The simulation results show the effectiveness of AUPF.

Dynamic Target Tracking Based on Particle Filter in Actual Environment

2013 ◽  
Vol 683 ◽  
pp. 824-827
Author(s):  
Tian Ding Chen ◽  
Chao Lu ◽  
Jian Hu
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Target Tracking ◽  
Monitoring System ◽  
Filter Method ◽  
Complex Scene ◽  
Actual Environment ◽  
Dynamic Target ◽  
Gaussian System ◽  
Non Gaussian

With the development of science and technology, target tracking was applied to many aspects of people's life, such as missile navigation, tanks localization, the plot monitoring system, robot field operation. Particle filter method dealing with the nonlinear and non-Gaussian system was widely used due to the complexity of the actual environment. This paper uses the resampling technology to reduce the particle degradation appeared in our test. Meanwhile, it compared particle filter with Kalman filter to observe their accuracy .The experiment results show that particle filter is more suitable for complex scene, so particle filter is more practical and feasible on target tracking.

Geophysical signal processing using sequential Bayesian techniques

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. V87-V100 ◽  
Author(s):  
Caglar Yardim ◽  
Peter Gerstoft ◽  
Zoi-Heleni Michalopoulou
Keyword(s):  
Posterior Probability ◽  
Signal To Noise Ratio ◽  
Multiple Model ◽  
Nonstationary Processes ◽  
Ensemble Kalman Filters ◽  
Bayesian Techniques ◽  
Strongly Nonlinear ◽  
Posterior Probability Density ◽  
Geophysical Signal ◽  
Seismic Measurements

Sequential Bayesian techniques enable tracking of evolving geophysical parameters via sequential observations. They provide a formulation in which the geophysical parameters that characterize dynamic, nonstationary processes are continuously estimated as new data become available. This is done by using prediction from previous estimates of geophysical parameters, updates stemming from physical and statistical models that relate seismic measurements to the unknown geophysical parameters. In addition, these techniques provide the evolving uncertainty in the estimates in the form of posterior probability density functions. In addition to the particle filters (PFs), extended, unscented, and ensemble Kalman filters (EnKFs) were evaluated. The filters were compared via reflector and nonvolcanic tremor tracking examples. Because there are numerous geophysical problems in which the environmental model itself is not known or evolves with time, the concept of model selection and its filtering implementation were introduced. A multiple model PF was then used to track an unknown number of reflectors from seismic interferometry data. We found that when the equations that define the geophysical problem are strongly nonlinear, a PF was needed. The PF outperformed all Kalman filter variants, especially in low signal-to-noise ratio tremor cases. However, PFs are computationally expensive. The EnKF is most appropriate when the number of parameters is large. Because each technique is ideal under different conditions, they complement each other and provide a useful set of techniques for solving sequential geophysical inversion problems.

Model order reduction of nonlinear eddy-current field using parameterized CLN

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Miwa Tobita ◽  
Hamed Eskandari ◽  
Tetsuji Matsuo
Keyword(s):  
Model Order Reduction ◽  
Dynamical Behavior ◽  
Order Reduction ◽  
Parameter Variation ◽  
Computational Time ◽  
State Equations ◽  
Model Order ◽  
Content Type ◽  
Parameter Variations ◽  
Nonlinear State

Purpose The authors derive a nonlinear MOR based on the Cauer ladder network (CLN) representation, which serves as an application of the parameterized MOR. Two parametrized CLN representations were developed to handle the nonlinear magnetic field. Simulations using the parameterized CLN were also conducted using an iron-cored inductor model under the first-order approximation. Design/methodology/approach This work studies the effect of parameter variations on reduced systems and aims at developing a general formulation for parametrized model order reduction (MOR) methods with the dynamical transition of parameterized state. Findings Terms including time derivatives of basis vectors appear in nonlinear state equations, in addition to the linear network equations of the CLN method. The terms are newly derived by an exact formulation of the parameterized CLN and are named parameter variation terms in this study. According to the simulation results, the parameter variation terms play a significant role in the nonlinear state equations when reluctivity is used, while they can be neglected when differential reluctivity is used. Practical implications The computational time of nonlinear transient analyses can be greatly reduced by applying the parameterized CLN when the number of time steps is large. Originality/value The authors introduced a general representation for the dynamical behavior of the reduced system with time-varying parameters, which has not been theoretically discussed in previous studies. The effect of the parameter variations is numerically given as a form of parameter variation terms by the exact derivation of the nonlinear state equations. The influence of parameter variation terms was confirmed by simulation.

scholarly journals Non-Gaussian Probability Densities of Convection Initiation and Development Investigated Using a Particle Filter with a Storm-Scale Numerical Weather Prediction Model

2019 ◽  
Vol 148 (1) ◽  
pp. 3-20 ◽  
Author(s):  
Takuya Kawabata ◽  
Genta Ueno
Keyword(s):  
Prediction Model ◽  
Particle Filter ◽  
Goodness Of Fit ◽  
Weather Prediction ◽  
Potential Temperature ◽  
Error Estimator ◽  
Observation Error ◽  
Adaptive Observation ◽  
Non Gaussian ◽  
Convection Initiation

Abstract Non-Gaussian probability density functions (PDFs) in convection initiation (CI) and development were investigated using a particle filter with a storm-scale numerical prediction model and an adaptive observation error estimator (NHM-RPF). An observing system simulation experiment (OSSE) was conducted with a 90-min assimilation period and 1000 particles at a 2-km grid spacing. Pseudosurface observations of potential temperature (PT), winds, water vapor (QV), and pseudoradar observations of rainwater (QR) in the lower troposphere were created in a nature run that simulated a well-developed cumulonimbus. The results of the OSSE (PF) show a significant improvement in comparison to ensemble simulations without any observations. The Gaussianity of the PDFs for PF in the CI area was evaluated using the Bayesian information criterion to compare goodness-of-fit of Gaussian, two-Gaussian mixture, and histogram models. The PDFs are strongly non-Gaussian when NHM-RPF produces diverse particles over the CI period. The non-Gaussian PDF of the updraft is followed by the upper-bounded PDF of the relative humidity, which produces non-Gaussian PDFs of QV and PT. The PDFs of the cloud water and QR are strongly non-Gaussian throughout the experimental period. We conclude that the non-Gaussianity of the CI originated from the non-Gaussianity of the updraft. In addition, we show that the adaptive observation error estimator significantly contributes to the stability of PF and the robustness to many observations.

Sign in / Sign up

Export Citation Format

Share Document